Statistics

Hey, can someone help me out with a probability problem?
So there are 14,662 undergraduate students, and 1,425 graduate students.

If we take a simple random sample of 10 students, what's the probability that the sample will contain two graduate students?

Then, let's say we take a randomly ordered list of students, and going down the list, we ask each student if they're a graduate student or an undergraduate. What's the chance that the 10th person we ask is our second graduate student?

This is a classic hypergeometric distribution application probability problem...

Let N = 14,662 undergraduate students and M = 1,425 graduate students.

The answer to the first question is simply all the possible combinations of 2 graduate students multiplied by all the possible combinations of the remaining 8 undergraduate students divided by the all possible combinations of 10 graduate and undergraduate students. The final formula is;

{{N \choose 8} {M \choose 2}} \over {{N+M} \choose 10}

The answer to the second question is a little bit more complex.

First you have to notice that "the chance that the 10th person is the second extracted graduated student" implies that you must have extracted 9 students (8 are undergraduate students and one is a graduate student, no matter the order) and then one graduate student (with probability 1 \over {M-1}).

The whole formula is:

{{{N \choose 8} {M \choose 1}} \over {{N+M} \choose 9}}*{1 \over {M-1}}